a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k,n-3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =8a(5) =29a(6) =86a(7) =224a(8) =554a(9) =1381a(10) =3556a(11) =9382a(12) =24901a(13) =65737a(14) =172321a(15) =450017a(16) =1174985a(17) =3072365a(18) =8044478a(19) =21074012a(20) =55199573a(21) =144535714a(22) =378366976a(23) =990441502a(24) =2592800365a(25) =6787973872a(26) =17771619370a(27) =46527959417a(28) =121813193825a(29) =318910531073